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arXiv · 1703.06445

Riesz Bounds of Spline Affine Systems

S. A. Chumachenko·S. F. Lukomskii·P. A. Terekhin
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Abstract

We construct a family of spline affine Riesz bases, i.e. sequences of dilations and translations generated by the special spline functions $ψ_m$, and we prove that their Riesz bounds are independent of $m$. We put $ψ_0=χ$ as the Haar step function and every following function $ψ_{m+1}$ is obtained by integrating the previous function $ψ_m$ with consequent antiperiodization. We give a representation of the spline $ψ_m$ as a finite sum of Rademacher chaos series and we use a notion of a simple Walsh spectrum of a function in connection with orthogonality of affine systems.

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S. A. Chumachenko, S. F. Lukomskii, P. A. Terekhin. 2017-03-19. Riesz Bounds of Spline Affine Systems. https://arxiv.org/abs/1703.06445

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